منابع مشابه
Complex Lorentzian Leech Lattice and Bimonster
We find 26 reflections in the automorphism group of the the Lorentzian Leech lattice L over Z[e] that form the Coxeter diagram seen in the presentation of the bimonster. We prove that these 26 reflections generate the automorphism group of L. We find evidence that these reflections behave like the simple roots and the vector fixed by the diagram automorphisms behaves like the Weyl vector for th...
متن کاملReflection Group of the Quaternionic Lorentzian Leech Lattice
We find 14 reflections in the automorphism group of the the quaternionic Lorentzian Leech lattice L that form the Coxeter diagram given by the incidence graph of projective plane over F2. We prove that these 14 reflections generate the automorphism group of L. We find evidence that these reflections behave like the simple roots and the vector fixed by the diagram automorphisms behaves like the ...
متن کاملThe complex Lorentzian Leech lattice and the bimonster
We find 26 reflections in the automorphism group of the the Lorentzian Leech lattice L over Z[e2πi/3] that form the Coxeter diagram seen in the presentation of the bimonster. We prove that these 26 reflections generate the automorphism group of L. We find evidence that these reflections behave like the simple roots and the vector fixed by the diagram automorphisms behaves like the Weyl vector f...
متن کاملThe Complex Lorentzian Leech Lattice and the Bimonster (ii)
Let D be the incidence graph of the projective plane over F3. The Artin group of the graph D maps onto the bimonster and a complex hyperbolic reflection group Γ acting on 13 dimensional complex hyperbolic space Y . The generators of the Artin group are mapped to elements of order 2 (resp. 3) in the bimonster (resp. Γ). Let Y ◦ ⊆ Y be the complement of the union of the fixed points of reflection...
متن کامل2 9 Ju n 20 06 Reflection group of the quaternionic Lorentzian Leech lattice
We study a second example of the phenomenon studied in the article “The complex Lorentzian Leech lattice and the bimonster”. We find 14 roots in the automorphism group of the the quaternionic Lorentzian Leech lattice L that form the Coxeter diagram given by the incidence graph of projective plane over F2. We prove that the reflections in these 14 roots generate the automorphism group of L. The ...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1982
ISSN: 0273-0979
DOI: 10.1090/s0273-0979-1982-14985-0